Cellular Automata: The Game of Life

The Game of Life is a 2D cellular automata where cells either “live” (turn black) or “die” (turn white) based on how many other cells around them are alive or dead. When you iterate, the cells interact to produce potentially complex patterns. Below is an interesting pattern that I found that is not chaotic but reproduces the initial set up..

Initial Condition: Starting with this pattern, it remains stable for infinite generations unless something is changed from the outside. When a living cell is added to any corner, the shape begins growing.

Generation 5: After 5 iterations, a very similar but much larger shape appears.

Generation 14: The initial shape has now blown up into this symmetrical “snow flake”

Generation 17: After 17 iterations, the initial shape has been reproduced into 4 exact versions of itself. If we were to add another living cell to a corner, the 4 would interact in a seemingly chaotic manner. However, this current pattern would stay stable for infinite iterations.